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"nothing," 1966, from earlier sense of "meaningless speech" (1960), originally Mr. Zilch (1931), comic character in the magazine "Ballyhoo." Perhaps from U.S. college slang (early 1900s) Joe Zilsch "an insignificant person." Probably a nonsense syllable, but Zilch is an actual German surname of Slavic origin.
Some sleep; a nap: If he wants a few zees we can go on automaticverb
To sleep; snooze; cop zs: Gotta Z a little while
[1960s+; fr the conventional sibilant or buzzing sound attributed to a sleeping or snoring person]